Download Phase-only hologram generation based on integral imaging and its

COL 9(12), 120009(2011)
CHINESE OPTICS LETTERS
December 10, 2011
Phase-only hologram generation based on integral imaging
and its enhancement in depth resolution
Jiwoon Yeom1 , Jisoo Hong1 , Jae-Hyun Jung1 , Keehoon Hong1 ,
Jae-Hyeung Park2 , and Byoungho Lee1∗
1
School of Electrical Engineering, Seoul National University, Gwanak-Gu Gwanakro 1, Seoul, 151-744, Korea
School of Information and Communication Engineering, Chungbuk National University, 410 SungBong-Ro,
Heungduk-Gu, Cheongju-Si, Chungbuk, 361-763, Korea
∗
Corresponding author: [email protected]
Received July 30, 2011; accepted September 27, 2011; posted online November 18, 2011
2
We introduce a phase-only hologram generation method based on an integral imaging, and propose an
enhancement method in representable depth interval. The computational integral imaging reconstruction
method is modified based on optical flow to obtain depth-slice images for the focused objects only. A phaseonly hologram for multiple plane images is generated using the iterative Fresnel transform algorithm. In
addition, a division method in hologram plane is proposed for enhancement in the representable minimum
depth interval.
OCIS codes: 090.0090, 100.0100.
doi: 10.3788/COL201109.120009.
Three-dimensional (3D) display is one of the most attractive fields in display technologies, and various methods
in processing 3D information have been widely studied[1] .
Among them is holography, which has been thought as
an ultimate method for describing 3D information since
it is capable of reconstructing the whole wavefront of a
recorded object wave. However, the recording process of
holography requires complicated and bulky experimental
setup, including coherent light sources. The requirement
for a well-aligned optical system makes it hard to capture
real objects outdoors.
Several researchers have adopted integral imaging (II)
to overcome the requirements in the capture process of
holography[2−4] . Since II provides a compact pickup
process in which 3D information is captured under an
incoherent light source, the high requirements of the traditional holography recording process can be alleviated.
Many researchers verified the performance of hologram
generated based on II using perspective view images or
orthographic view images as the source of information.
In our previous research[4] , we proposed a compact
method for making the phase-only hologram of 3D objects using computational II reconstruction (CIIR) and
iterative Fresnel transform algorithm (IFTA), as shown
in Fig. 1. One of merits in this study is that the computer
generated hologram (CGH) only has phase profile with
constant amplitude distribution. Since phase-only modulation devices are widely used due to their efficiency, it
is an important issue to make constant amplitude profile
in the CGH. To satisfy the constant amplitude distribution, we used the modified IFTA for the multi-plane
images[5] .
In this letter, we verify the limitation of our previous
work, and propose an enhancement method for generating hologram with higher depth resolution. The modified
CIIR method for obtaining depth-slice images without
blurred ones based on optical flow is discussed. In addition, space multiplexing in hologram plane is adopted to
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improve the representable depth interval. The simulation and experimental results are provided to verify the
proposed method.
In the pickup process of II, 3D objects are captured
through the lens array as a form of elemental image
set. The elemental image set contains various perspective images, which are captured at different positions.
From this property, the elemental image set is applied
for other purposes such as depth map calculation[6,7] ,
occluded region reconstruction[7] , and depth-slice image
generation[8,9] . We use the elemental image set for the
purpose of generating depth-slice images, which is the
basic information for multi-plane phase-only hologram[4] .
The individual depth-slice image is placed at the proper
Fig. 1. Overall process of hologram generation based on II.
FT: Fresnel transform.
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c 2011 Chinese Optics Letters
°
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CHINESE OPTICS LETTERS
depth plane and converted into phase-only hologram
using IFTA for multiple planes[5] . In the IFTA, each
target image is propagated into the next depth plane,
and the phase distribution in the complex amplitude of
the propagated wave is extracted to be combined with
the new target image. During the process, propagation
over distance z is performed using the Fresnel diffraction
integral[10] . At the hologram plane, the constant amplitude condition is forced, and the phase profile of the
hologram is propagated to image planes with inverse
direction. This process is repeated until the CGH has
almost constant amplitude.
The basic CIIR used in the previous hologram generation method is not suitable for generating exact depthslice images because the unfocused object leads to blurred
images. In general, the depth-slice image must contain
only the information of the focused part in the object.
However, images generated based on the basic CIIR
method contain not only information on the focused objects, but also on the unfocused ones. To demonstrate
an example of the basic CIIR method, we captured two
objects that were located at a distance of 40 and 70 mm
away from the lens array, as shown in Fig. 2(a). Figures
3(a) and (b) show the depth-slice images using the basic
CIIR method based on the estimated depth map of Fig.
2(b). In the depth-slice image for the first object, Fig.
3(a), the blurred version of the second object image is
shown and vice versa. These blurred images are one
of the reasons for the image degradation of the reconstructed images of the hologram.
In addition, it is not possible to represent the correct
target images in the CGH if the interval between adjacent depth planes is too small. Figure 4(a) shows the
CGH, while Figs. 4(b) and (c) show the numerical reconstruction results with depth interval of 5 mm. The
focal length of Fourier transform (FT) lens, f , is assumed
to be 100 mm. We used CIIR images provided in Figs.
3(c) and (d), which are generated based on the modified
CIIR method which is discussed later. Since our goal
is to examine the effect of small depth interval on the
reconstructed image quality, it is necessary to minimize
the effect of the blurred images due to the unfocused
objects with the modified CIIR method. As shown in
Fig. 4(c), which is the reconstructed result of the second target image, ghost images of the first target image
exist. In the same manner, some parts of the second
target image are shown in Fig. 4(b). These ghost images are different from the blurred portion in the CIIR
images, as shown in Figs. 3(a) and (b). They occur because the depth interval between two planes, ∆z, is too
small[5] . This problem becomes severe as the distance
between the two depth planes becomes smaller. Although
Fig. 2. Overall pickup process. (a) Experimental setup and
(b) extracted depth map.
December 10, 2011
Fig. 3. CIIR images with basic CIIR method at (a) z1 = 40
mm and (b) z2 = 70 mm, and with modified CIIR method at
(c) z1 = 40 mm and (d) z2 = 70 mm.
Fig. 4. Hologram generation process. (a) CGH without hologram division method and its numerically reconstructed images at (b) z1 = 40 mm and (c) z2 = 45 mm; (d) CGH with
hologram division method and its numerically reconstructed
images at (e) z1 = 40 mm and (f) z2 = 45 mm.
we eliminate the blurred parts due to the unfocused objects in the CIIR method, the overlapped images can still
appear as the distance between adjacent planes becomes
closer.
Figure 5(a) presents the peak signal-to-noise ratio
(PSNR) values according to ∆z when f is equal to 100,
150, and 200 mm. In the figure legend of Fig. 5(a),
“case I” means the PSNR values in the case of undivided hologram, and “case II” refers to the PSNR values
with the hologram division method. The PSNR values
of the numerically reconstructed images with undivided
hologram decrease as ∆z is decreased, because the pixels
of the hologram represent different information at each
depth. The wave propagated from the hologram plane
reconstructs the first target CIIR image at z = z1 . The
reconstructed wavefront is considered to be the superposition of spherical waves emitted from each pixel of the
hologram plane with diverse phase delays. If ∆z is too
small, the change in each phase delay term is not enough.
Because of the insufficient change in each phase delay,
the new wavefront at z2 = z1 + ∆z fails to represent
the second target CIIR image without the afterimage of
the first one. This is the reason of the existence of the
ghost images of the other target images with small depth
interval.
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CHINESE OPTICS LETTERS
Fig. 5. Simulation results. (a) PSNR values according to the
depth interval and (b) minimum representable depth interval
with various focal length of the FT lens.
An important factor that determines the minimum
depth interval in adjacent depth planes without ghost
images, ∆zmin , is the focal length of the FT lens. To verify the relationship between f and ∆zmin , we performed
a simulation using a black image with a point light source
as the first target image and empty black image as the
second target image. If ∆z is small, the ghost image of
the point source is also shown in the reconstructed second target image. The ∆zmin is defined as the interval
of adjacent planes when the intensity of the ghost image
of the point source in the second target image is equal to
the half value of the intensity of the original one. In the
simulation, f and ∆z vary from 50 to 250 mm with the
interval of 50 mm, and from 5 to 100 mm with interval
of 5 mm, respectively. Figure 5(b) shows the simulation
results performed with the two target images of 100 ×
100 pixels. This confirms that the FT lens with lower
focal length provides smaller ∆zmin if other parameters
remain unchanged. This result coincides with the previous simulation result provided in Fig. 5(a), which verifies
that the PSNR value has higher value with lower f .
To suppress the blurred portion of the CIIR images,
we estimate the depth of each object based on the optical flow in Ref. [7], and modify the elemental image set
for each object. In Ref. [7], the depth extraction and
occluded region reconstruction are performed for the orthographic images. However, since the orthographic images have all-in-focus property, they are rearranged and
converted into perspective images for generating CIIR
images. We assume plane objects for simplicity, and the
estimated depth is obtained using the disparity shown in
the elemental image set. The original elemental image
set can be divided into multiple elemental image sets according to the object’s depth by using the appropriate
depth threshold. The new elemental image sets contain
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only the information of one object, and the blurred portion due to the unfocused objects can be eliminated in
the modified CIIR images.
However, if the overlapped region between the objects
is too large, it is impossible to generate the correct depthslice images because of the lack of information captured
in the elemental image set. In Ref. [7], the authors provided the limitation range in the occluded region that
can be reconstructed, which also becomes the limitation
region in the modified CIIR method.
We generated CIIR images based on the proposed
method with the elemental image set captured in the experimental setup of Fig. 2(a) to verify the effect of suppression for the unfocused objects in our CIIR method.
The two elemental image sets are newly generated using the estimated depth map provided in Fig. 2(b), and
the CIIR images for each object’s depth are generated as
shown in Figs. 3(c) and (d). Comparing this with the
previous CIIR images, the undesirable part in each CIIR
image due to the unfocused object is eliminated.
As discussed previously, the FT lens with low focal
length is necessary to display the target images with
small depth interval. Instead of using low focal length FT
lens, another possible approach to provide small depth
interval is to divide the hologram plane and allocate the
different holograms of each depth-slice image. The hologram plane is composed of the spatial frequency component of the target images. Therefore, if we divide this
spatial frequency domain and assign different holograms,
we can represent each hologram respectively.
Unlike in the previous method, each CIIR image in the
proposed approach has its own hologram. This means
that the N number of phase holograms is generated for
representing the N number of CIIR images. The resultant synthesized hologram Hsyn is composed of multiple
sub-holograms for each depth-slice image. If we have two
CIIR images and the hologram of the first and second
CIIR images are represented as H1 and H2 , respectively,
the division in spatial frequency is demonstrated as
½
H1 (x, y), xy > 0
Hsyn (x, y) =
.
(1)
H2 (x, y), xy < 0
In Eq. (1), the position of the (0,0) point is the center
of the spatial light modulator (SLM) plane. Figures 4(e)
and (f) show the numerically reconstructed results from
the hologram provided in Fig. 4(d). The distance between the two target images is the same as those in Figs.
4(b) and (c). However, unlike those in Figs. 4(b) and
(c) in which ghost images appear, the reconstructed images in Figs. 4(e) and (f) present desirable target images
without ghost images.
The PSNR values according to ∆z are provided in
Fig. 5(a) for the reconstructed images with the proposed
hologram division method. The PSNR values decrease
as ∆z is decreased without the division in the hologram plane. However, by using hologram division in the
proposed method, the PSNR values become almost constant regardless of the decrease in ∆z. With the large
value of ∆z, the PSNR values without hologram division
are higher than those with hologram division because
there is loss in spatial frequency component in the latter.
However, below a certain level of ∆z, it is not possible
to represent the correct target images for the hologram
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CHINESE OPTICS LETTERS
without division. The proposed method can provide the
individual target image without ghost images.
For the optical reconstruction of the generated hologram, a laser with wavelength of 532 nm is used as a light
source and f is 100 mm. We used a phase-only SLM by
Holoeye (LC 2002 model), and the maximum resolution
is 800 × 600 with pixel pitch of 32 µm. Figure 6 presents
the optically reconstructed results with 5 mm of depth
interval for the case of undivided and divided hologram,
respectively. In Fig. 6(a), the first target image of the
object “box” appears with the ghost image of the second
target image, which is not reconstructed well. The low
figures show that both the first and second target images
are reconstructed successfully with the proposed method.
Although we did not use the elimination method for the
zero-order diffracted light from the SLM, the quality of
the optically reconstructed image is enhanced with the
use of high-pass filter[11] . We can verify from the experimental results that the CGH using the proposed method
can represent the depth-slice images of real objects with
small depth interval.
Although the division in the hologram plane shows
good results compared with the undivided case, the quality of the image reconstructed from the divided hologram
is degraded as the number of division increases. Figure
7 shows the variation of the PSNR values according to
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the number of division, N , in the hologram plane when
the depth interval is 5 mm and f is equal to 100 mm. In
this simulation, the synthesized hologram is composed
of N number of sub-holograms, which satisfy the radial
shapes. Since the PSNR value for 5 mm of depth interval and 100 mm of focal length without the hologram
division method is around 38 dB, the maximum number
of target images allowed is up to six. However, the maximum number of division depends on how the hologram
plane is divided, and this can be enhanced if the method
for hologram division is optimized.
In conclusion, we introduce a hologram generation
method based on II, and propose an enhancement
method for depth interval limitation without ghost images. In the CIIR process, the original elemental image
set is modified based on the estimated depth of objects to
remove the blurred image due to the unfocused object. In
addition, we examine the effect of depth interval between
adjacent planes on the quality of the reconstructed images. The hologram plane is divided and assigned with
the holograms for each depth-slice image to overcome
the limitation in depth interval. The principle of the
proposed method is verified in the simulation and experiment results, confirming its feasibility. Further research
related to the analytical study of representable depth interval and the optimization for hologram plane division
will be required.
This work was supported by the Brain Korea 21 Program (Information Technology of Seoul National University).
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Fig. 6. Optically reconstructed images with 5 mm depthinterval in the case of (a) undivided hologram and (b) divided
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